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Intensities of Hyperfine Components in Saturation Spectroscopy

J. Bordb

Published Jul 8, 2015• 0 citations
OpenAlex

Abstract

A theory is presented for the intensities of hyperfine components in saturation spectroscopy. We use a diagrammatic approach to nonlinear processes to derive closed-form formulas for the intensities of recoil doublets and of Doppler-generated level crossings. We discuss the influence of the terms introduced by hyperfine coherences in saturation spectroscopy. We also demonstrate spectroscopic stability when the hyperfine splittings are negligible. A catalog of simple formulas is given in view of applications to current spectroscopy and is illustrated by recent examples, including Doppler-free polarization spectroscopy. The extension to other sub-Doppler techniques such as two-photon Doppler-free spectroscopy is outlined. I.

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A theory is presented for the intensities of hyperfine components in saturation spectroscopy. We use a diagrammatic approach to nonlinear processes to derive closed-form formulas for the intensities of recoil doublets and of Doppler-generated level crossings. We discuss the influence of the terms introduced by hyperfine coherences in saturation spectroscopy. We also demonstrate spectroscopic stability when the hyperfine splittings are negligible. A catalog of simple formulas is given in view of applications to current spectroscopy and is illustrated by recent examples, including Doppler-free polarization spectroscopy. The extension to other sub-Doppler techniques such as two-photon Doppler-free spectroscopy is outlined. I.
Previously derived equations describing recoil effects in saturated absorption by a gas of two-level atoms or molecules are solved numerically for the case of standing plane-wave excitation and large Doppler broadening. The numerical techniques and accuracy estimates are discussed briefly. The lineshapes obtained are well approximated by the superposition of two Lorentzian functions whose width, heights, and separation parametrise the lineshape. The dependence of these parameters on saturation, recoil splitting, and relaxation rates is described and compared with corresponding results in the rate equation approximation and in the weak-probe-beam approximation. Saturation broadening depends strongly on these latter approximations, but very little on recoil splitting. When multiphoton processes are retained in the equations, increasing saturation causes a slight decrease in the fitted separation of the peaks. The ratio of the heights of the two Lorentzians is closely related to the ratio of relaxation rates for the level populations.
We report in this paper the principle of the calculation of the hyperfine components of a two-photon absorption line and we compare the results of the calculation with some of our expérimental results. In the first part of the paper, the two-photon transition operator is expanded on a tensorial irreductible set basis. That operator is generally the sum of two operators, one scalar and the other one quadrupolar. We deduce from it the selection rules for two-photon absorption and the formulae which permit one to calculate the intensities of the hyperfine components of a two-photon absorption line. We also report the density matrix in the excited state obtained after the two-photon excitation process, which permits one to calculate the fluorescence lines. At last we present the atomic quantities involved in the collision broadening of a two-photon absorption line. In the second part, we present the experimental hyperfine spectra obtained on the neon 21 atom for the transitions between the 3s[3/2] 2 metastable level and the 4d'[5/2] 2, 4d'[3/2] 2 and 4d[3/2] 2 excited levels. We show that the expérimental ratios between the scalar and the quadrupolar parts are very different from one transition to another. At last we compare these ratios with theoretical values obtained using the formulae of the first part. We find a good agreement between expérimental and theoretical values.
The relative intensities of the Doppler-free signals in the transition from polarized and dispersive signals to absorptive signals of the Na D1 line are calculated theoretically from the approximation of a single cycle of opticalpumping in a four-level system. The transition from polarized signals to saturated signals is made by varying the angle of an analyzer. Since the signal in polarization spectroscopy is mixed with the signal in saturation spectroscopy during the transition, spurious signals due to saturation and polarization effects should be taken into account in the signal analysis of polarization and saturation spectroscopies, respectively. Both theories, of polarization spectroscopy and saturation spectroscopy are unified and applied to the Doppler-free signals of the Na D1 line. The results obtained from the four-level optical pumping theory which mixes polarization spectroscopy with saturation spectroscopy are in good agreement with experimental reports.
We report the first observation of the recoil shift of an optical resonance in the visible part of the spectrum. The method rests on the fact that the recoil shifts have opposite signs for Doppler-generated level crossings with a common upper level and for those having a common lower level. The experiment has been performed with the argon laser at 5145 \AA{} as the source and iodine as the absorber. The measured values are within 12% of the theoretical recoil shift. We give a detailed discussion of the possible influence of shifts of various origins and especially light shifts on the measured frequency differences. We display saturated absorption and saturated dispersion spectra and give formulas for the intensities of the various resonances derived from the corresponding density-matrix diagrams.
Abstract In this chapter, we explore the clever spectroscopy technique known as saturated absorption spectroscopy. This technique is used to remove Doppler profiles from spectroscopic signals. We will learn how saturated absorption spectroscopy works, including the roles of probe and pump beams, and the resulting spectral features. Additionally, we will examine the artifacts, specifically crossover features (V , Λ\Lambda Λ Λ , and X crossovers), that may appear due to this technique and understand the conditions under which they occur. Practical examples using various atoms, advanced techniques for achieving crossover-free spectroscopy, and potential issues are also discussed.
We present a theoretical analysis of high-frequency optical heterodyne saturation spectroscopy in Doppler-broadened coupled three-level systems. The saturating beam, which is assumed to be amplitude modulated at frequency δ (double-sideband suppressed carrier amplitude modulation) is resonant for one of the transitions. Through non-degenerate four-wave mixing processes, this modulation is transferred to a probe beam, resonant for the coupled transition. Saturating and probe fields may be either co-propagating or counter-propagating. The lineshape of the probe modulation is analysed via a third-order perturbation expansion of the atomic density matrix with respect to the incident field amplitudes. The resulting signal is integrated over velocities, in the Doppler limit approximation. Both population saturation effects and coherent (Raman-type, or two-photon) processes contribute to the signal. The various contributions appear as Lorentzian-type resonance doublets. We show that, in the absence of relaxation processes (collisional dephasing, or radiative cascades), destructive interferences between population saturation and coherent two-photon processes are responsible for the disappearance of one resonance doublet. Phase-interrupting collisions are thus predicted to lead to the existence of a « pressure-induced extra-resonance » (PIER) doublet, which could yield information on collisional processes in the impact regime. The properties of the predicted PIER doublets are analysed in relation with other types of PIER signals studied in four-wave mixing, and in time-resolved saturation spectroscopy.